From the web site,
"Functional data analysis, which lots of us like to call "FDA", is
about the analysis of information on curves or functions. [...] FDA
is a collection statistical techniques for answering questions like,
"What are the main ways in which the curves vary from one writing to
another?" In fact, most of the questions and problems associated with
the usual multivariate data analyzed by statistical packages like SAS
and SPSS have their functional counterparts. But what is unique about
functional data is the possibility of also using information on the
rates of change or derivatives of the curves."

No mention of Stata. But from reading some of the pages on this site,
the term, "functional data analysis" is not very informative, and I'm
sure Stata could be used if you had something specific in mind.

Functional analysis, if I'm understanding the web site content, has
also made its way into gene mapping. It goes by the term "functional
QTL mapping". Functional QTL mapping puts a biologically motivated
mathematical function between genetic and phenoypic variation. Like
growth or drug response or circadian rhythm functions (curves). I am
interested in this field, related to drug genetics, and in this area,
canned nonlinear models are useful functions for the gene mapping,
rather than a set of basis functions. Another personal interest in
growth (proliferation of cells) may be better handled with spline
basis functions. Perhaps the spline function command recently (re)
written by Bill Dupont could be adapted (rc_spline.ado). Interesting
post!